## anonymous 5 years ago Find the sum of the geometric series. 5 Σ 2(-4)k k=1

1. anonymous

is that (-4)^k or (-4)*k

2. anonymous

since its geometric, ill assume k is the exponent 2 is a constant so it can be pulled out of sum formula for sum of geometric sequence is $s _{n}=\frac{a _{1}(1-r ^{n})}{1-r}$ r = -4, n =5, a=-4 s = -4(1-(-4)^5)/(1-(-4)) s = -4(1+1024)/5 s = -820

3. anonymous

oops then multiply by 2 s = -820*2 s=-1640

4. anonymous

but wait a min, since it's a geometric series, you'lk have to take the absolute value of r , |r| = |-4| = 4 >1, in this case, since R > 1 then the following series is said to diverge, right? .-.